Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,2,Mod(35,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 13]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.35");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.l (of order \(18\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.58715302549\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 143.7 | ||
Character | \(\chi\) | \(=\) | 324.143 |
Dual form | 324.2.l.a.179.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{7}{18}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.438668 | + | 1.34446i | −0.310185 | + | 0.950676i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.61514 | − | 1.17954i | −0.807570 | − | 0.589771i | ||||
\(5\) | −3.32285 | + | 0.585909i | −1.48603 | + | 0.262026i | −0.856983 | − | 0.515344i | \(-0.827664\pi\) |
−0.629043 | + | 0.777371i | \(0.716553\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.72640 | − | 2.05745i | 0.652519 | − | 0.777641i | −0.333773 | − | 0.942653i | \(-0.608322\pi\) |
0.986292 | + | 0.165012i | \(0.0527663\pi\) | |||||||
\(8\) | 2.29436 | − | 1.65406i | 0.811178 | − | 0.584800i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.669899 | − | 4.72446i | 0.211841 | − | 1.49401i | ||||
\(11\) | 0.506730 | − | 2.87381i | 0.152785 | − | 0.866486i | −0.807998 | − | 0.589185i | \(-0.799449\pi\) |
0.960783 | − | 0.277301i | \(-0.0894400\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.552703 | + | 0.201167i | 0.153292 | + | 0.0557938i | 0.417527 | − | 0.908665i | \(-0.362897\pi\) |
−0.264234 | + | 0.964458i | \(0.585119\pi\) | |||||||
\(14\) | 2.00883 | + | 3.22361i | 0.536884 | + | 0.861547i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.21736 | + | 3.81025i | 0.304340 | + | 0.952563i | ||||
\(17\) | 6.36286 | − | 3.67360i | 1.54322 | − | 0.890979i | 0.544588 | − | 0.838704i | \(-0.316686\pi\) |
0.998633 | − | 0.0522747i | \(-0.0166472\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.82795 | − | 1.63272i | −0.648776 | − | 0.374571i | 0.139211 | − | 0.990263i | \(-0.455543\pi\) |
−0.787987 | + | 0.615692i | \(0.788877\pi\) | |||||||
\(20\) | 6.05798 | + | 2.97312i | 1.35461 | + | 0.664810i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.64143 | + | 1.94193i | 0.776356 | + | 0.414020i | ||||
\(23\) | 0.365077 | − | 0.306336i | 0.0761238 | − | 0.0638754i | −0.603932 | − | 0.797036i | \(-0.706400\pi\) |
0.680056 | + | 0.733161i | \(0.261956\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.99961 | − | 2.18368i | 1.19992 | − | 0.436736i | ||||
\(26\) | −0.512914 | + | 0.654840i | −0.100591 | + | 0.128425i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5.21523 | + | 1.28670i | −0.985585 | + | 0.243164i | ||||
\(29\) | −1.49502 | − | 4.10753i | −0.277618 | − | 0.762749i | −0.997631 | − | 0.0687888i | \(-0.978087\pi\) |
0.720013 | − | 0.693960i | \(-0.244136\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.73778 | − | 4.45451i | −0.671325 | − | 0.800054i | 0.317639 | − | 0.948212i | \(-0.397110\pi\) |
−0.988964 | + | 0.148158i | \(0.952666\pi\) | |||||||
\(32\) | −5.65675 | − | 0.0347450i | −0.999981 | − | 0.00614210i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.14782 | + | 10.1661i | 0.368348 | + | 1.74347i | ||||
\(35\) | −4.53111 | + | 7.84811i | −0.765897 | + | 1.32657i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.59532 | − | 2.76318i | −0.262269 | − | 0.454264i | 0.704575 | − | 0.709629i | \(-0.251138\pi\) |
−0.966845 | + | 0.255365i | \(0.917804\pi\) | |||||||
\(38\) | 3.43565 | − | 3.08584i | 0.557336 | − | 0.500589i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.65468 | + | 6.84050i | −1.05220 | + | 1.08158i | ||||
\(41\) | 1.09875 | − | 3.01880i | 0.171596 | − | 0.471457i | −0.823847 | − | 0.566812i | \(-0.808177\pi\) |
0.995443 | + | 0.0953554i | \(0.0303987\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.79304 | + | 0.316161i | 0.273436 | + | 0.0482141i | 0.308685 | − | 0.951164i | \(-0.400111\pi\) |
−0.0352488 | + | 0.999379i | \(0.511222\pi\) | |||||||
\(44\) | −4.20822 | + | 4.04390i | −0.634413 | + | 0.609641i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.251708 | + | 0.625211i | 0.0371124 | + | 0.0921823i | ||||
\(47\) | −0.940800 | − | 0.789425i | −0.137230 | − | 0.115149i | 0.571589 | − | 0.820540i | \(-0.306327\pi\) |
−0.708819 | + | 0.705391i | \(0.750772\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.0370819 | − | 0.210302i | −0.00529741 | − | 0.0300431i | ||||
\(50\) | 0.304032 | + | 9.02414i | 0.0429965 | + | 1.27621i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.655407 | − | 0.976849i | −0.0908886 | − | 0.135465i | ||||
\(53\) | 7.37157i | 1.01256i | 0.862368 | + | 0.506282i | \(0.168980\pi\) | ||||
−0.862368 | + | 0.506282i | \(0.831020\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.84615i | 1.32765i | ||||||||
\(56\) | 0.557836 | − | 7.57609i | 0.0745440 | − | 1.01240i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.17822 | − | 0.208150i | 0.811240 | − | 0.0273314i | ||||
\(59\) | −0.718733 | − | 4.07614i | −0.0935710 | − | 0.530668i | −0.995176 | − | 0.0981070i | \(-0.968721\pi\) |
0.901605 | − | 0.432561i | \(-0.142390\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.421725 | + | 0.353869i | 0.0539963 | + | 0.0453083i | 0.669386 | − | 0.742914i | \(-0.266557\pi\) |
−0.615390 | + | 0.788223i | \(0.711002\pi\) | |||||||
\(62\) | 7.62855 | − | 3.07124i | 0.968827 | − | 0.390048i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.52815 | − | 7.59002i | 0.316018 | − | 0.948753i | ||||
\(65\) | −1.95442 | − | 0.344616i | −0.242415 | − | 0.0427444i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.46492 | − | 9.51978i | 0.423307 | − | 1.16303i | −0.526496 | − | 0.850178i | \(-0.676495\pi\) |
0.949803 | − | 0.312849i | \(-0.101283\pi\) | |||||||
\(68\) | −14.6101 | − | 1.57188i | −1.77173 | − | 0.190619i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −8.56381 | − | 9.53460i | −1.02357 | − | 1.13960i | ||||
\(71\) | −0.616505 | − | 1.06782i | −0.0731657 | − | 0.126727i | 0.827121 | − | 0.562023i | \(-0.189977\pi\) |
−0.900287 | + | 0.435297i | \(0.856644\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.18077 | − | 2.04515i | 0.138198 | − | 0.239366i | −0.788616 | − | 0.614885i | \(-0.789202\pi\) |
0.926815 | + | 0.375519i | \(0.122536\pi\) | |||||||
\(74\) | 4.41480 | − | 0.932727i | 0.513210 | − | 0.108427i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.64168 | + | 5.97275i | 0.303021 | + | 0.685121i | ||||
\(77\) | −5.03789 | − | 6.00392i | −0.574121 | − | 0.684210i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.33584 | + | 9.16514i | 0.375311 | + | 1.03116i | 0.973276 | + | 0.229637i | \(0.0737538\pi\) |
−0.597965 | + | 0.801522i | \(0.704024\pi\) | |||||||
\(80\) | −6.27757 | − | 11.9477i | −0.701854 | − | 1.33579i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.57666 | + | 2.80148i | 0.394976 | + | 0.309371i | ||||
\(83\) | −16.8988 | + | 6.15067i | −1.85489 | + | 0.675124i | −0.872401 | + | 0.488790i | \(0.837438\pi\) |
−0.982487 | + | 0.186333i | \(0.940340\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −18.9905 | + | 15.9349i | −2.05981 | + | 1.72838i | ||||
\(86\) | −1.21161 | + | 2.27198i | −0.130652 | + | 0.244994i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.59084 | − | 7.43171i | −0.382785 | − | 0.792223i | ||||
\(89\) | 4.81205 | + | 2.77824i | 0.510076 | + | 0.294493i | 0.732865 | − | 0.680374i | \(-0.238183\pi\) |
−0.222789 | + | 0.974867i | \(0.571516\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.36808 | − | 0.789860i | 0.143413 | − | 0.0827998i | ||||
\(92\) | −0.950986 | + | 0.0641520i | −0.0991472 | + | 0.00668831i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.47405 | − | 0.918571i | 0.152036 | − | 0.0947434i | ||||
\(95\) | 10.3535 | + | 3.76836i | 1.06224 | + | 0.386626i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.83865 | − | 10.4275i | 0.186687 | − | 1.05875i | −0.737082 | − | 0.675803i | \(-0.763797\pi\) |
0.923769 | − | 0.382951i | \(-0.125092\pi\) | |||||||
\(98\) | 0.299009 | + | 0.0423976i | 0.0302045 | + | 0.00428280i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −12.2660 | − | 3.54984i | −1.22660 | − | 0.354984i | ||||
\(101\) | −5.49760 | + | 6.55178i | −0.547032 | + | 0.651927i | −0.966749 | − | 0.255728i | \(-0.917685\pi\) |
0.419717 | + | 0.907655i | \(0.362129\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.7001 | + | 2.94469i | −1.64551 | + | 0.290149i | −0.918189 | − | 0.396144i | \(-0.870348\pi\) |
−0.727326 | + | 0.686292i | \(0.759237\pi\) | |||||||
\(104\) | 1.60084 | − | 0.452656i | 0.156975 | − | 0.0443865i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.91078 | − | 3.23367i | −0.962620 | − | 0.314082i | ||||
\(107\) | 3.73466 | 0.361043 | 0.180522 | − | 0.983571i | \(-0.442221\pi\) | ||||
0.180522 | + | 0.983571i | \(0.442221\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.6061 | 1.01588 | 0.507940 | − | 0.861393i | \(-0.330407\pi\) | ||||
0.507940 | + | 0.861393i | \(0.330407\pi\) | |||||||
\(110\) | −13.2377 | − | 4.31919i | −1.26217 | − | 0.411819i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 9.94104 | + | 4.07338i | 0.939340 | + | 0.384898i | ||||
\(113\) | 5.75136 | − | 1.01412i | 0.541042 | − | 0.0954004i | 0.103553 | − | 0.994624i | \(-0.466979\pi\) |
0.437489 | + | 0.899224i | \(0.355868\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.03361 | + | 1.23181i | −0.0963848 | + | 0.114867i | ||||
\(116\) | −2.43034 | + | 8.39768i | −0.225651 | + | 0.779705i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.79548 | + | 0.821763i | 0.533517 | + | 0.0756494i | ||||
\(119\) | 3.42662 | − | 19.4333i | 0.314118 | − | 1.78145i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.33461 | + | 0.849729i | 0.212237 | + | 0.0772481i | ||||
\(122\) | −0.660760 | + | 0.411761i | −0.0598224 | + | 0.0372791i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.782755 | + | 11.6035i | 0.0702935 | + | 1.04203i | ||||
\(125\) | −4.04606 | + | 2.33599i | −0.361890 | + | 0.208937i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.06513 | − | 0.614951i | −0.0945147 | − | 0.0545681i | 0.451998 | − | 0.892019i | \(-0.350712\pi\) |
−0.546512 | + | 0.837451i | \(0.684045\pi\) | |||||||
\(128\) | 9.09546 | + | 6.72849i | 0.803933 | + | 0.594720i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.32066 | − | 2.47646i | 0.115830 | − | 0.217200i | ||||
\(131\) | 13.5213 | − | 11.3457i | 1.18136 | − | 0.991278i | 0.181390 | − | 0.983411i | \(-0.441940\pi\) |
0.999969 | − | 0.00786658i | \(-0.00250404\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.24140 | + | 2.99962i | −0.714620 | + | 0.260100i | ||||
\(134\) | 11.2790 | + | 8.83446i | 0.974358 | + | 0.763181i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.52231 | − | 18.9531i | 0.730782 | − | 1.62522i | ||||
\(137\) | 3.54986 | + | 9.75317i | 0.303285 | + | 0.833269i | 0.993924 | + | 0.110069i | \(0.0351073\pi\) |
−0.690639 | + | 0.723200i | \(0.742671\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.0279 | + | 16.7178i | 1.18983 | + | 1.41798i | 0.885009 | + | 0.465573i | \(0.154152\pi\) |
0.304820 | + | 0.952410i | \(0.401404\pi\) | |||||||
\(140\) | 16.5756 | − | 7.33117i | 1.40089 | − | 0.619597i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.70608 | − | 0.360448i | 0.143171 | − | 0.0302482i | ||||
\(143\) | 0.858188 | − | 1.48642i | 0.0717653 | − | 0.124301i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.37437 | + | 12.7728i | 0.612408 | + | 1.06072i | ||||
\(146\) | 2.23165 | + | 2.48463i | 0.184693 | + | 0.205630i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.682616 | + | 6.34467i | −0.0561107 | + | 0.521529i | ||||
\(149\) | −1.27723 | + | 3.50915i | −0.104635 | + | 0.287481i | −0.980951 | − | 0.194255i | \(-0.937771\pi\) |
0.876317 | + | 0.481736i | \(0.159993\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.3762 | + | 2.53492i | 1.16992 | + | 0.206289i | 0.724657 | − | 0.689110i | \(-0.241998\pi\) |
0.445265 | + | 0.895399i | \(0.353109\pi\) | |||||||
\(152\) | −9.18894 | + | 0.931571i | −0.745321 | + | 0.0755604i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 10.2820 | − | 4.13951i | 0.828546 | − | 0.333571i | ||||
\(155\) | 15.0300 | + | 12.6117i | 1.20724 | + | 1.01300i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.89506 | − | 16.4187i | −0.231051 | − | 1.31036i | −0.850773 | − | 0.525534i | \(-0.823866\pi\) |
0.619722 | − | 0.784822i | \(-0.287245\pi\) | |||||||
\(158\) | −13.7855 | + | 0.464445i | −1.09671 | + | 0.0369493i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 18.8169 | − | 3.19889i | 1.48761 | − | 0.252894i | ||||
\(161\) | − | 1.27998i | − | 0.100877i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.78256i | 0.217947i | 0.994045 | + | 0.108973i | \(0.0347563\pi\) | ||||
−0.994045 | + | 0.108973i | \(0.965244\pi\) | |||||||
\(164\) | −5.33544 | + | 3.57976i | −0.416628 | + | 0.279532i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.856352 | − | 25.4179i | −0.0664658 | − | 1.97281i | ||||
\(167\) | 2.46126 | + | 13.9585i | 0.190458 | + | 1.08014i | 0.918740 | + | 0.394863i | \(0.129208\pi\) |
−0.728282 | + | 0.685278i | \(0.759681\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.69357 | − | 8.13387i | −0.745659 | − | 0.625682i | ||||
\(170\) | −13.0933 | − | 32.5220i | −1.00421 | − | 2.49433i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.52308 | − | 2.62561i | −0.192383 | − | 0.200201i | ||||
\(173\) | −1.21493 | − | 0.214226i | −0.0923698 | − | 0.0162873i | 0.127272 | − | 0.991868i | \(-0.459378\pi\) |
−0.219642 | + | 0.975581i | \(0.570489\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.86494 | − | 16.1138i | 0.443348 | − | 1.21809i | ||||
\(176\) | 11.5668 | − | 1.56769i | 0.871882 | − | 0.118169i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.84612 | + | 5.25088i | −0.438185 | + | 0.393570i | ||||
\(179\) | 8.60015 | + | 14.8959i | 0.642805 | + | 1.11337i | 0.984804 | + | 0.173671i | \(0.0555630\pi\) |
−0.341998 | + | 0.939701i | \(0.611104\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.8176 | + | 18.7366i | −0.804065 | + | 1.39268i | 0.112855 | + | 0.993611i | \(0.464000\pi\) |
−0.916920 | + | 0.399071i | \(0.869333\pi\) | |||||||
\(182\) | 0.461803 | + | 2.18581i | 0.0342311 | + | 0.162023i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.330918 | − | 1.30670i | 0.0243956 | − | 0.0963315i | ||||
\(185\) | 6.91999 | + | 8.24693i | 0.508768 | + | 0.606326i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.33297 | − | 20.1472i | −0.536240 | − | 1.47331i | ||||
\(188\) | 0.588364 | + | 2.38474i | 0.0429109 | + | 0.173925i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −9.60815 | + | 12.2668i | −0.697048 | + | 0.889925i | ||||
\(191\) | 4.48414 | − | 1.63210i | 0.324461 | − | 0.118094i | −0.174654 | − | 0.984630i | \(-0.555881\pi\) |
0.499115 | + | 0.866536i | \(0.333658\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.94036 | − | 5.82365i | 0.499578 | − | 0.419196i | −0.357866 | − | 0.933773i | \(-0.616496\pi\) |
0.857444 | + | 0.514577i | \(0.172051\pi\) | |||||||
\(194\) | 13.2128 | + | 7.04621i | 0.948625 | + | 0.505888i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.188167 | + | 0.383407i | −0.0134405 | + | 0.0273862i | ||||
\(197\) | −1.80241 | − | 1.04062i | −0.128416 | − | 0.0741411i | 0.434416 | − | 0.900712i | \(-0.356955\pi\) |
−0.562832 | + | 0.826571i | \(0.690288\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.74989 | + | 5.62910i | −0.691151 | + | 0.399036i | −0.804043 | − | 0.594571i | \(-0.797322\pi\) |
0.112892 | + | 0.993607i | \(0.463989\pi\) | |||||||
\(200\) | 10.1533 | − | 14.9339i | 0.717947 | − | 1.05598i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.39699 | − | 10.2654i | −0.450090 | − | 0.722268i | ||||
\(203\) | −11.0320 | − | 4.01533i | −0.774296 | − | 0.281821i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.88225 | + | 10.6748i | −0.131462 | + | 0.745560i | ||||
\(206\) | 3.36681 | − | 23.7444i | 0.234577 | − | 1.65435i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.0936603 | + | 2.35083i | −0.00649417 | + | 0.163001i | ||||
\(209\) | −6.12512 | + | 7.29964i | −0.423684 | + | 0.504926i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.42064 | − | 0.955805i | 0.373172 | − | 0.0658003i | 0.0160832 | − | 0.999871i | \(-0.494880\pi\) |
0.357089 | + | 0.934070i | \(0.383769\pi\) | |||||||
\(212\) | 8.69508 | − | 11.9061i | 0.597181 | − | 0.817716i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.63828 | + | 5.02110i | −0.111990 | + | 0.343235i | ||||
\(215\) | −6.14325 | −0.418966 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.6178 | −1.06021 | ||||||||
\(218\) | −4.65255 | + | 14.2595i | −0.315111 | + | 0.965773i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 11.6140 | − | 15.9029i | 0.783012 | − | 1.07217i | ||||
\(221\) | 4.25578 | − | 0.750408i | 0.286275 | − | 0.0504779i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.51114 | − | 4.18441i | 0.235123 | − | 0.280209i | −0.635562 | − | 0.772050i | \(-0.719231\pi\) |
0.870685 | + | 0.491841i | \(0.163676\pi\) | |||||||
\(224\) | −9.83731 | + | 11.5785i | −0.657283 | + | 0.773619i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.15949 | + | 8.17733i | −0.0771284 | + | 0.543948i | ||||
\(227\) | 0.257802 | − | 1.46207i | 0.0171109 | − | 0.0970410i | −0.975056 | − | 0.221958i | \(-0.928755\pi\) |
0.992167 | + | 0.124917i | \(0.0398664\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.4836 | + | 8.91131i | 1.61792 | + | 0.588876i | 0.982985 | − | 0.183688i | \(-0.0588035\pi\) |
0.634938 | + | 0.772563i | \(0.281026\pi\) | |||||||
\(230\) | −1.20271 | − | 1.93001i | −0.0793042 | − | 0.127261i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.2242 | − | 6.95128i | −0.671253 | − | 0.456374i | ||||
\(233\) | −5.81401 | + | 3.35672i | −0.380889 | + | 0.219906i | −0.678205 | − | 0.734873i | \(-0.737242\pi\) |
0.297316 | + | 0.954779i | \(0.403908\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.58867 | + | 2.07192i | 0.234099 | + | 0.135157i | ||||
\(236\) | −3.64712 | + | 7.43131i | −0.237407 | + | 0.483737i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 24.6242 | + | 13.1317i | 1.59615 | + | 0.851204i | ||||
\(239\) | −15.7014 | + | 13.1750i | −1.01564 | + | 0.852223i | −0.989073 | − | 0.147424i | \(-0.952902\pi\) |
−0.0265665 | + | 0.999647i | \(0.508457\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.8674 | + | 4.31940i | −0.764449 | + | 0.278237i | −0.694673 | − | 0.719326i | \(-0.744451\pi\) |
−0.0697765 | + | 0.997563i | \(0.522229\pi\) | |||||||
\(242\) | −2.16654 | + | 2.76604i | −0.139271 | + | 0.177808i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.263741 | − | 1.06899i | −0.0168843 | − | 0.0684351i | ||||
\(245\) | 0.246436 | + | 0.677076i | 0.0157442 | + | 0.0432568i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.23456 | − | 1.47130i | −0.0785535 | − | 0.0936164i | ||||
\(248\) | −15.9438 | − | 4.03771i | −1.01243 | − | 0.256395i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.36577 | − | 6.46448i | −0.0863789 | − | 0.408850i | ||||
\(251\) | 6.38939 | − | 11.0668i | 0.403295 | − | 0.698527i | −0.590827 | − | 0.806799i | \(-0.701198\pi\) |
0.994121 | + | 0.108272i | \(0.0345316\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.695355 | − | 1.20439i | −0.0437166 | − | 0.0757194i | ||||
\(254\) | 1.29401 | − | 1.16226i | 0.0811936 | − | 0.0729266i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −13.0361 | + | 9.27690i | −0.814754 | + | 0.579806i | ||||
\(257\) | 3.40030 | − | 9.34225i | 0.212105 | − | 0.582754i | −0.787324 | − | 0.616539i | \(-0.788534\pi\) |
0.999429 | + | 0.0337856i | \(0.0107563\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.43926 | − | 1.48807i | −0.524390 | − | 0.0924641i | ||||
\(260\) | 2.75017 | + | 2.86192i | 0.170558 | + | 0.177489i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.32247 | + | 23.1558i | 0.575944 | + | 1.43057i | ||||
\(263\) | −14.9780 | − | 12.5681i | −0.923586 | − | 0.774981i | 0.0510689 | − | 0.998695i | \(-0.483737\pi\) |
−0.974655 | + | 0.223715i | \(0.928182\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.31907 | − | 24.4947i | −0.265318 | − | 1.50470i | ||||
\(266\) | −0.417634 | − | 12.3961i | −0.0256068 | − | 0.760051i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −16.8253 | + | 11.2888i | −1.02777 | + | 0.689571i | ||||
\(269\) | − | 30.3293i | − | 1.84921i | −0.380930 | − | 0.924604i | \(-0.624396\pi\) | ||
0.380930 | − | 0.924604i | \(-0.375604\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 19.1257i | − | 1.16181i | −0.813973 | − | 0.580903i | \(-0.802699\pi\) | ||
0.813973 | − | 0.580903i | \(-0.197301\pi\) | |||||||
\(272\) | 21.7432 | + | 19.7720i | 1.31838 | + | 1.19885i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.6699 | + | 0.494244i | −0.886244 | + | 0.0298583i | ||||
\(275\) | −3.23530 | − | 18.3483i | −0.195096 | − | 1.10644i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.54011 | + | 6.32690i | 0.453041 | + | 0.380147i | 0.840563 | − | 0.541714i | \(-0.182224\pi\) |
−0.387522 | + | 0.921861i | \(0.626669\pi\) | |||||||
\(278\) | −28.6299 | + | 11.5264i | −1.71711 | + | 0.691305i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.58529 | + | 25.5011i | 0.154501 | + | 1.52398i | ||||
\(281\) | 22.8259 | + | 4.02483i | 1.36168 | + | 0.240101i | 0.806306 | − | 0.591499i | \(-0.201463\pi\) |
0.555375 | + | 0.831600i | \(0.312575\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.96637 | + | 16.3925i | −0.354664 | + | 0.974432i | 0.626187 | + | 0.779673i | \(0.284615\pi\) |
−0.980851 | + | 0.194759i | \(0.937608\pi\) | |||||||
\(284\) | −0.263794 | + | 2.45187i | −0.0156533 | + | 0.145492i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.62198 | + | 1.80584i | 0.0959096 | + | 0.106782i | ||||
\(287\) | −4.31412 | − | 7.47228i | −0.254655 | − | 0.441075i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 18.4907 | − | 32.0268i | 1.08769 | − | 1.88393i | ||||
\(290\) | −20.4074 | + | 4.31153i | −1.19836 | + | 0.253182i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.31944 | + | 1.91044i | −0.252776 | + | 0.111800i | ||||
\(293\) | −12.2291 | − | 14.5741i | −0.714431 | − | 0.851426i | 0.279646 | − | 0.960103i | \(-0.409783\pi\) |
−0.994077 | + | 0.108678i | \(0.965338\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.77649 | + | 13.1233i | 0.278098 | + | 0.764068i | ||||
\(296\) | −8.23071 | − | 3.70095i | −0.478400 | − | 0.215114i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.15763 | − | 3.25653i | −0.240845 | − | 0.188646i | ||||
\(299\) | 0.263404 | − | 0.0958711i | 0.0152330 | − | 0.00554437i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.74599 | − | 3.14326i | 0.215915 | − | 0.181174i | ||||
\(302\) | −9.71449 | + | 18.2163i | −0.559006 | + | 1.04823i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.77843 | − | 12.7628i | 0.159354 | − | 0.731997i | ||||
\(305\) | −1.60867 | − | 0.928763i | −0.0921119 | − | 0.0531808i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.3110 | + | 8.26248i | −0.816773 | + | 0.471564i | −0.849303 | − | 0.527906i | \(-0.822977\pi\) |
0.0325291 | + | 0.999471i | \(0.489644\pi\) | |||||||
\(308\) | 1.05502 | + | 15.6396i | 0.0601154 | + | 0.891148i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −23.5491 | + | 14.6749i | −1.33750 | + | 0.833479i | ||||
\(311\) | −1.95536 | − | 0.711694i | −0.110879 | − | 0.0403565i | 0.285985 | − | 0.958234i | \(-0.407679\pi\) |
−0.396864 | + | 0.917878i | \(0.629901\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.0264293 | + | 0.149888i | −0.00149387 | + | 0.00847218i | −0.985546 | − | 0.169410i | \(-0.945814\pi\) |
0.984052 | + | 0.177883i | \(0.0569248\pi\) | |||||||
\(314\) | 23.3442 | + | 3.31007i | 1.31739 | + | 0.186798i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.42282 | − | 18.7377i | 0.305057 | − | 1.05408i | ||||
\(317\) | 4.31448 | − | 5.14180i | 0.242325 | − | 0.288792i | −0.631150 | − | 0.775661i | \(-0.717417\pi\) |
0.873475 | + | 0.486869i | \(0.161861\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.5618 | + | 2.21499i | −0.703327 | + | 0.124016i | ||||
\(320\) | −3.95360 | + | 26.7018i | −0.221013 | + | 1.49268i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.72089 | + | 0.561488i | 0.0959013 | + | 0.0312905i | ||||
\(323\) | −23.9918 | −1.33494 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.75529 | 0.208306 | ||||||||
\(326\) | −3.74103 | − | 1.22062i | −0.207197 | − | 0.0676038i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.47235 | − | 8.74360i | −0.136513 | − | 0.482785i | ||||
\(329\) | −3.24840 | + | 0.572780i | −0.179090 | + | 0.0315784i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.49106 | + | 10.1192i | −0.466711 | + | 0.556204i | −0.947136 | − | 0.320831i | \(-0.896038\pi\) |
0.480426 | + | 0.877035i | \(0.340482\pi\) | |||||||
\(332\) | 34.5490 | + | 9.99868i | 1.89612 | + | 0.548749i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −19.8463 | − | 2.81408i | −1.08594 | − | 0.153980i | ||||
\(335\) | −5.93569 | + | 33.6630i | −0.324301 | + | 1.83920i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.1807 | + | 6.61722i | 0.990364 | + | 0.360463i | 0.785861 | − | 0.618403i | \(-0.212220\pi\) |
0.204503 | + | 0.978866i | \(0.434442\pi\) | |||||||
\(338\) | 15.1879 | − | 9.46454i | 0.826113 | − | 0.514803i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 49.4682 | − | 3.33704i | 2.68279 | − | 0.180976i | ||||
\(341\) | −14.6955 | + | 8.48443i | −0.795804 | + | 0.459458i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.7851 | + | 9.11354i | 0.852316 | + | 0.492085i | ||||
\(344\) | 4.63682 | − | 2.24041i | 0.250001 | − | 0.120795i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.820971 | − | 1.53946i | 0.0441357 | − | 0.0827617i | ||||
\(347\) | −9.79587 | + | 8.21971i | −0.525870 | + | 0.441257i | −0.866672 | − | 0.498878i | \(-0.833746\pi\) |
0.340803 | + | 0.940135i | \(0.389301\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.3836 | − | 4.14328i | 0.609348 | − | 0.221785i | −0.0188700 | − | 0.999822i | \(-0.506007\pi\) |
0.628218 | + | 0.778037i | \(0.283785\pi\) | |||||||
\(350\) | 19.0916 | + | 14.9538i | 1.02049 | + | 0.799313i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.96630 | + | 16.2388i | −0.158104 | + | 0.865532i | ||||
\(353\) | −6.82994 | − | 18.7651i | −0.363521 | − | 0.998766i | −0.977775 | − | 0.209657i | \(-0.932765\pi\) |
0.614254 | − | 0.789108i | \(-0.289457\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.67420 | + | 3.18699i | 0.141932 | + | 0.169148i | ||||
\(356\) | −4.49509 | − | 10.1633i | −0.238239 | − | 0.538652i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −23.7995 | + | 5.02820i | −1.25784 | + | 0.265749i | ||||
\(359\) | 10.5259 | − | 18.2314i | 0.555535 | − | 0.962214i | −0.442327 | − | 0.896854i | \(-0.645847\pi\) |
0.997862 | − | 0.0653605i | \(-0.0208197\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.16848 | − | 7.22001i | −0.219393 | − | 0.380001i | ||||
\(362\) | −20.4453 | − | 22.7630i | −1.07458 | − | 1.19639i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.14131 | − | 0.337970i | −0.164649 | − | 0.0177144i | ||||
\(365\) | −2.72524 | + | 7.48755i | −0.142646 | + | 0.391916i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −27.4150 | − | 4.83400i | −1.43105 | − | 0.252333i | −0.596211 | − | 0.802828i | \(-0.703328\pi\) |
−0.834838 | + | 0.550495i | \(0.814439\pi\) | |||||||
\(368\) | 1.61165 | + | 1.01811i | 0.0840129 | + | 0.0530729i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −14.1232 | + | 5.68599i | −0.734232 | + | 0.295600i | ||||
\(371\) | 15.1666 | + | 12.7263i | 0.787411 | + | 0.660717i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.03662 | + | 5.87895i | 0.0536740 | + | 0.304400i | 0.999813 | − | 0.0193617i | \(-0.00616340\pi\) |
−0.946139 | + | 0.323762i | \(0.895052\pi\) | |||||||
\(374\) | 30.3038 | − | 1.02096i | 1.56697 | − | 0.0527927i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.46429 | − | 0.255079i | −0.178657 | − | 0.0131547i | ||||
\(377\) | − | 2.57099i | − | 0.132413i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 14.2394i | − | 0.731429i | −0.930727 | − | 0.365715i | \(-0.880825\pi\) | ||
0.930727 | − | 0.365715i | \(-0.119175\pi\) | |||||||
\(380\) | −12.2774 | − | 18.2988i | −0.629817 | − | 0.938709i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.227235 | + | 6.74470i | 0.0116263 | + | 0.345089i | ||||
\(383\) | 2.77843 | + | 15.7573i | 0.141971 | + | 0.805159i | 0.969749 | + | 0.244103i | \(0.0784935\pi\) |
−0.827778 | + | 0.561056i | \(0.810395\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 20.2579 | + | 16.9984i | 1.03244 | + | 0.866319i | ||||
\(386\) | 4.78515 | + | 11.8857i | 0.243558 | + | 0.604965i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −15.2694 | + | 14.6731i | −0.775185 | + | 0.744916i | ||||
\(389\) | −17.5295 | − | 3.09093i | −0.888782 | − | 0.156716i | −0.289427 | − | 0.957200i | \(-0.593465\pi\) |
−0.599355 | + | 0.800484i | \(0.704576\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.19758 | − | 3.29032i | 0.0605641 | − | 0.166399i | ||||
\(392\) | −0.432932 | − | 0.421172i | −0.0218664 | − | 0.0212724i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.18973 | − | 1.96678i | 0.110317 | − | 0.0990847i | ||||
\(395\) | −16.4544 | − | 28.4999i | −0.827913 | − | 1.43399i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.34449 | + | 16.1851i | −0.468987 | + | 0.812309i | −0.999372 | − | 0.0354484i | \(-0.988714\pi\) |
0.530385 | + | 0.847757i | \(0.322047\pi\) | |||||||
\(398\) | −3.29113 | − | 15.5776i | −0.164970 | − | 0.780836i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 15.6241 | + | 20.2017i | 0.781203 | + | 1.01009i | ||||
\(401\) | 19.8603 | + | 23.6686i | 0.991778 | + | 1.18195i | 0.983300 | + | 0.181991i | \(0.0582541\pi\) |
0.00847759 | + | 0.999964i | \(0.497301\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.16978 | − | 3.21394i | −0.0582708 | − | 0.160098i | ||||
\(404\) | 16.6075 | − | 4.09740i | 0.826254 | − | 0.203853i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.2378 | − | 13.0707i | 0.508095 | − | 0.648688i | ||||
\(407\) | −8.74925 | + | 3.18447i | −0.433684 | + | 0.157848i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.8560 | + | 15.8220i | −0.932368 | + | 0.782349i | −0.976241 | − | 0.216688i | \(-0.930475\pi\) |
0.0438734 | + | 0.999037i | \(0.486030\pi\) | |||||||
\(410\) | −13.5261 | − | 7.21330i | −0.668008 | − | 0.356240i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 30.4465 | + | 14.9424i | 1.49999 | + | 0.736161i | ||||
\(413\) | −9.62725 | − | 5.55829i | −0.473726 | − | 0.273506i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 52.5486 | − | 30.3390i | 2.57951 | − | 1.48928i | ||||
\(416\) | −3.11951 | − | 1.15716i | −0.152947 | − | 0.0567342i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7.12717 | − | 11.4371i | −0.348601 | − | 0.559407i | ||||
\(419\) | 7.48245 | + | 2.72339i | 0.365542 | + | 0.133046i | 0.518259 | − | 0.855224i | \(-0.326580\pi\) |
−0.152718 | + | 0.988270i | \(0.548802\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.713817 | + | 4.04826i | −0.0347893 | + | 0.197300i | −0.997249 | − | 0.0741247i | \(-0.976384\pi\) |
0.962460 | + | 0.271425i | \(0.0874948\pi\) | |||||||
\(422\) | −1.09282 | + | 7.70711i | −0.0531977 | + | 0.375176i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12.1931 | + | 16.9130i | 0.592147 | + | 0.821369i | ||||
\(425\) | 30.1527 | − | 35.9346i | 1.46262 | − | 1.74309i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.45613 | − | 0.256755i | 0.0704672 | − | 0.0124253i | ||||
\(428\) | −6.03201 | − | 4.40519i | −0.291568 | − | 0.212933i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.69485 | − | 8.25935i | 0.129957 | − | 0.398301i | ||||
\(431\) | 34.6402 | 1.66856 | 0.834281 | − | 0.551340i | \(-0.185883\pi\) | ||||
0.834281 | + | 0.551340i | \(0.185883\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.55521 | −0.411137 | −0.205569 | − | 0.978643i | \(-0.565904\pi\) | ||||
−0.205569 | + | 0.978643i | \(0.565904\pi\) | |||||||
\(434\) | 6.85104 | − | 20.9975i | 0.328860 | − | 1.00791i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −17.1303 | − | 12.5103i | −0.820394 | − | 0.599137i | ||||
\(437\) | −1.53258 | + | 0.270235i | −0.0733131 | + | 0.0129271i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.14956 | + | 6.13700i | −0.245775 | + | 0.292903i | −0.874802 | − | 0.484480i | \(-0.839009\pi\) |
0.629027 | + | 0.777383i | \(0.283453\pi\) | |||||||
\(440\) | 16.2862 | + | 22.5906i | 0.776412 | + | 1.07696i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.857980 | + | 6.05090i | −0.0408099 | + | 0.287812i | ||||
\(443\) | 1.37913 | − | 7.82143i | 0.0655244 | − | 0.371607i | −0.934359 | − | 0.356333i | \(-0.884027\pi\) |
0.999883 | − | 0.0152741i | \(-0.00486210\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −17.6175 | − | 6.41226i | −0.835151 | − | 0.303970i | ||||
\(446\) | 4.08555 | + | 6.55615i | 0.193456 | + | 0.310443i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −11.2515 | − | 18.3050i | −0.531582 | − | 0.864828i | ||||
\(449\) | −0.748371 | + | 0.432072i | −0.0353178 | + | 0.0203907i | −0.517555 | − | 0.855650i | \(-0.673158\pi\) |
0.482237 | + | 0.876041i | \(0.339824\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.11868 | − | 4.68732i | −0.382294 | − | 0.220717i | ||||
\(452\) | −10.4855 | − | 5.14603i | −0.493194 | − | 0.242049i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.85260 | + | 0.987968i | 0.0869470 | + | 0.0463676i | ||||
\(455\) | −4.08314 | + | 3.42616i | −0.191420 | + | 0.160621i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.5979 | − | 10.0448i | 1.29098 | − | 0.469877i | 0.396930 | − | 0.917849i | \(-0.370076\pi\) |
0.894048 | + | 0.447972i | \(0.147853\pi\) | |||||||
\(458\) | −22.7211 | + | 29.0081i | −1.06169 | + | 1.35546i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.12240 | − | 0.770359i | 0.145583 | − | 0.0359182i | ||||
\(461\) | 1.96584 | + | 5.40111i | 0.0915585 | + | 0.251555i | 0.977016 | − | 0.213165i | \(-0.0683772\pi\) |
−0.885458 | + | 0.464720i | \(0.846155\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.6836 | + | 21.0745i | 0.821825 | + | 0.979413i | 0.999989 | − | 0.00458769i | \(-0.00146031\pi\) |
−0.178164 | + | 0.984001i | \(0.557016\pi\) | |||||||
\(464\) | 13.8308 | − | 10.6967i | 0.642077 | − | 0.496584i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.96255 | − | 9.28919i | −0.0909136 | − | 0.430313i | ||||
\(467\) | −8.41790 | + | 14.5802i | −0.389534 | + | 0.674692i | −0.992387 | − | 0.123160i | \(-0.960697\pi\) |
0.602853 | + | 0.797852i | \(0.294031\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.6046 | − | 23.5638i | −0.628202 | − | 1.08808i | ||||
\(470\) | −4.35985 | + | 3.91594i | −0.201105 | + | 0.180629i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8.39122 | − | 8.16328i | −0.386237 | − | 0.375745i | ||||
\(473\) | 1.81717 | − | 4.99264i | 0.0835537 | − | 0.229562i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20.5319 | − | 3.62033i | −0.942069 | − | 0.166112i | ||||
\(476\) | −28.4569 | + | 27.3457i | −1.30432 | + | 1.25339i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −10.8256 | − | 26.8894i | −0.495152 | − | 1.22989i | ||||
\(479\) | −1.69205 | − | 1.41980i | −0.0773119 | − | 0.0648724i | 0.603313 | − | 0.797505i | \(-0.293847\pi\) |
−0.680625 | + | 0.732632i | \(0.738292\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.325877 | − | 1.84814i | −0.0148587 | − | 0.0842680i | ||||
\(482\) | −0.601385 | − | 17.8501i | −0.0273923 | − | 0.813049i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.76843 | − | 4.12620i | −0.125838 | − | 0.187555i | ||||
\(485\) | 35.7264i | 1.62225i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 40.4859i | − | 1.83459i | −0.398206 | − | 0.917296i | \(-0.630367\pi\) | ||
0.398206 | − | 0.917296i | \(-0.369633\pi\) | |||||||
\(488\) | 1.55291 | + | 0.114342i | 0.0702969 | + | 0.00517604i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.01840 | + | 0.0343110i | −0.0460068 | + | 0.00155001i | ||||
\(491\) | −2.74760 | − | 15.5824i | −0.123998 | − | 0.703225i | −0.981898 | − | 0.189409i | \(-0.939343\pi\) |
0.857901 | − | 0.513816i | \(-0.171768\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −24.6020 | − | 20.6435i | −1.10802 | − | 0.929738i | ||||
\(494\) | 2.51966 | − | 1.01441i | 0.113365 | − | 0.0456405i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.4226 | − | 19.6646i | 0.557791 | − | 0.882968i | ||||
\(497\) | −3.26131 | − | 0.575058i | −0.146290 | − | 0.0257949i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.4425 | − | 31.4380i | 0.512236 | − | 1.40736i | −0.366665 | − | 0.930353i | \(-0.619501\pi\) |
0.878901 | − | 0.477004i | \(-0.158277\pi\) | |||||||
\(500\) | 9.29035 | + | 0.999538i | 0.415477 | + | 0.0447007i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.0760 | + | 13.4449i | 0.538977 | + | 0.600075i | ||||
\(503\) | 12.0161 | + | 20.8125i | 0.535772 | + | 0.927984i | 0.999126 | + | 0.0418106i | \(0.0133126\pi\) |
−0.463354 | + | 0.886173i | \(0.653354\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.4290 | − | 24.9917i | 0.642081 | − | 1.11212i | ||||
\(506\) | 1.92428 | − | 0.406549i | 0.0855449 | − | 0.0180733i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.994968 | + | 2.24959i | 0.0441446 | + | 0.0998096i | ||||
\(509\) | 15.9558 | + | 19.0154i | 0.707228 | + | 0.842841i | 0.993324 | − | 0.115360i | \(-0.0368022\pi\) |
−0.286096 | + | 0.958201i | \(0.592358\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.16930 | − | 5.96011i | −0.0959643 | − | 0.263660i | ||||
\(512\) | −6.75391 | − | 21.5959i | −0.298484 | − | 0.954415i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 11.0687 | + | 8.66972i | 0.488218 | + | 0.382405i | ||||
\(515\) | 53.7669 | − | 19.5695i | 2.36925 | − | 0.862337i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.74539 | + | 2.30365i | −0.120742 | + | 0.101315i | ||||
\(518\) | 5.70268 | − | 10.6935i | 0.250561 | − | 0.469844i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.05415 | + | 2.44206i | −0.221639 | + | 0.107091i | ||||
\(521\) | 13.6964 | + | 7.90761i | 0.600049 | + | 0.346439i | 0.769061 | − | 0.639175i | \(-0.220724\pi\) |
−0.169012 | + | 0.985614i | \(0.554058\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.0410 | + | 15.6122i | −1.18242 | + | 0.682672i | −0.956574 | − | 0.291491i | \(-0.905849\pi\) |
−0.225849 | + | 0.974162i | \(0.572515\pi\) | |||||||
\(524\) | −35.2215 | + | 2.37598i | −1.53866 | + | 0.103795i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23.4676 | − | 14.6242i | 1.02324 | − | 0.637644i | ||||
\(527\) | −40.1470 | − | 14.6123i | −1.74883 | − | 0.636523i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.95447 | + | 22.4269i | −0.171933 | + | 0.975083i | ||||
\(530\) | 34.8267 | + | 4.93821i | 1.51278 | + | 0.214502i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 16.8492 | + | 4.87626i | 0.730506 | + | 0.211413i | ||||
\(533\) | 1.21457 | − | 1.44746i | 0.0526087 | − | 0.0626966i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.4097 | + | 2.18817i | −0.536520 | + | 0.0946029i | ||||
\(536\) | −7.79657 | − | 27.5730i | −0.336760 | − | 1.19097i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 40.7765 | + | 13.3045i | 1.75800 | + | 0.573597i | ||||
\(539\) | −0.623158 | −0.0268413 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.4554 | −0.621486 | −0.310743 | − | 0.950494i | \(-0.600578\pi\) | ||||
−0.310743 | + | 0.950494i | \(0.600578\pi\) | |||||||
\(542\) | 25.7138 | + | 8.38985i | 1.10450 | + | 0.360375i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −36.1207 | + | 20.5595i | −1.54866 | + | 0.881483i | ||||
\(545\) | −35.2425 | + | 6.21421i | −1.50962 | + | 0.266187i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.0006 | − | 27.4110i | 0.983434 | − | 1.17201i | −0.00166132 | − | 0.999999i | \(-0.500529\pi\) |
0.985095 | − | 0.172012i | \(-0.0550267\pi\) | |||||||
\(548\) | 5.77074 | − | 19.9400i | 0.246514 | − | 0.851792i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 26.0877 | + | 3.69908i | 1.11238 | + | 0.157729i | ||||
\(551\) | −2.47860 | + | 14.0568i | −0.105592 | + | 0.598841i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.6158 | + | 8.95941i | 1.04677 | + | 0.380993i | ||||
\(554\) | −11.8139 | + | 7.36196i | −0.501923 | + | 0.312780i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.93768 | − | 43.5480i | −0.124585 | − | 1.84685i | ||||
\(557\) | 25.5879 | − | 14.7732i | 1.08419 | − | 0.625960i | 0.152170 | − | 0.988354i | \(-0.451374\pi\) |
0.932025 | + | 0.362394i | \(0.118041\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.927416 | + | 0.535444i | 0.0392255 | + | 0.0226469i | ||||
\(560\) | −35.4193 | − | 7.71069i | −1.49674 | − | 0.325836i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15.4242 | + | 28.9230i | −0.650632 | + | 1.22004i | ||||
\(563\) | 8.84941 | − | 7.42554i | 0.372958 | − | 0.312949i | −0.436972 | − | 0.899475i | \(-0.643949\pi\) |
0.809930 | + | 0.586526i | \(0.199505\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.5168 | + | 6.73955i | −0.779006 | + | 0.283535i | ||||
\(566\) | −19.4218 | − | 15.2124i | −0.816358 | − | 0.639425i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.18072 | − | 1.43022i | −0.133460 | − | 0.0600106i | ||||
\(569\) | −4.36916 | − | 12.0042i | −0.183165 | − | 0.503241i | 0.813796 | − | 0.581151i | \(-0.197397\pi\) |
−0.996960 | + | 0.0779103i | \(0.975175\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.8893 | + | 29.6619i | 1.04158 | + | 1.24131i | 0.969803 | + | 0.243890i | \(0.0784235\pi\) |
0.0717799 | + | 0.997420i | \(0.477132\pi\) | |||||||
\(572\) | −3.13939 | + | 1.38852i | −0.131265 | + | 0.0580568i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 11.9386 | − | 2.52231i | 0.498309 | − | 0.105279i | ||||
\(575\) | 1.52138 | − | 2.63511i | 0.0634459 | − | 0.109892i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.5964 | + | 18.3535i | 0.441134 | + | 0.764067i | 0.997774 | − | 0.0666873i | \(-0.0212430\pi\) |
−0.556640 | + | 0.830754i | \(0.687910\pi\) | |||||||
\(578\) | 34.9474 | + | 38.9091i | 1.45362 | + | 1.61840i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.15539 | − | 29.3282i | 0.131020 | − | 1.21779i | ||||
\(581\) | −16.5195 | + | 45.3870i | −0.685344 | + | 1.88297i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21.1845 | + | 3.73540i | 0.877372 | + | 0.154704i | ||||
\(584\) | −0.673704 | − | 6.64536i | −0.0278781 | − | 0.274987i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 24.9587 | − | 10.0483i | 1.03104 | − | 0.415093i | ||||
\(587\) | 11.6298 | + | 9.75855i | 0.480013 | + | 0.402778i | 0.850431 | − | 0.526087i | \(-0.176341\pi\) |
−0.370418 | + | 0.928865i | \(0.620786\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.29729 | + | 18.6999i | 0.135862 | + | 0.770514i | ||||
\(590\) | −19.7390 | + | 0.665025i | −0.812643 | + | 0.0273787i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.58633 | − | 9.44236i | 0.352896 | − | 0.388079i | ||||
\(593\) | 25.8789i | 1.06272i | 0.847147 | + | 0.531359i | \(0.178319\pi\) | ||||
−0.847147 | + | 0.531359i | \(0.821681\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 66.5819i | 2.72959i | ||||||||
\(596\) | 6.20209 | − | 4.16123i | 0.254048 | − | 0.170451i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.0133480 | + | 0.396191i | 0.000545841 | + | 0.0162015i | ||||
\(599\) | 0.0271904 | + | 0.154204i | 0.00111097 | + | 0.00630062i | 0.985358 | − | 0.170497i | \(-0.0545373\pi\) |
−0.984247 | + | 0.176798i | \(0.943426\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.42031 | + | 2.86998i | 0.139517 | + | 0.117069i | 0.709875 | − | 0.704327i | \(-0.248751\pi\) |
−0.570358 | + | 0.821396i | \(0.693196\pi\) | |||||||
\(602\) | 2.58274 | + | 6.41517i | 0.105264 | + | 0.261463i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −20.2296 | − | 21.0516i | −0.823131 | − | 0.856579i | ||||
\(605\) | −8.25544 | − | 1.45566i | −0.335631 | − | 0.0591808i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.8586 | + | 35.3287i | −0.521914 | + | 1.43395i | 0.346474 | + | 0.938060i | \(0.387379\pi\) |
−0.868387 | + | 0.495886i | \(0.834843\pi\) | |||||||
\(608\) | 15.9403 | + | 9.33412i | 0.646463 | + | 0.378549i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.95435 | − | 1.75537i | 0.0791295 | − | 0.0710727i | ||||
\(611\) | −0.361176 | − | 0.625575i | −0.0146116 | − | 0.0253081i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.84356 | + | 17.0495i | −0.397577 | + | 0.688624i | −0.993426 | − | 0.114472i | \(-0.963482\pi\) |
0.595849 | + | 0.803096i | \(0.296816\pi\) | |||||||
\(614\) | −4.83077 | − | 22.8651i | −0.194954 | − | 0.922759i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −21.4896 | − | 5.44215i | −0.865840 | − | 0.219270i | ||||
\(617\) | −14.8351 | − | 17.6798i | −0.597241 | − | 0.711764i | 0.379740 | − | 0.925093i | \(-0.376014\pi\) |
−0.976980 | + | 0.213330i | \(0.931569\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.717110 | + | 1.97024i | 0.0288231 | + | 0.0791908i | 0.953270 | − | 0.302121i | \(-0.0976947\pi\) |
−0.924447 | + | 0.381312i | \(0.875472\pi\) | |||||||
\(620\) | −9.39959 | − | 38.0982i | −0.377497 | − | 1.53006i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.81460 | − | 2.31671i | 0.0727588 | − | 0.0928916i | ||||
\(623\) | 14.0236 | − | 5.10417i | 0.561844 | − | 0.204494i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.3789 | + | 10.3871i | −0.495155 | + | 0.415484i | ||||
\(626\) | −0.189925 | − | 0.101284i | −0.00759092 | − | 0.00404813i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14.6906 | + | 29.9334i | −0.586220 | + | 1.19447i | ||||
\(629\) | −20.3016 | − | 11.7211i | −0.809479 | − | 0.467353i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.15935 | − | 2.40140i | 0.165581 | − | 0.0955982i | −0.414920 | − | 0.909858i | \(-0.636190\pi\) |
0.580500 | + | 0.814260i | \(0.302857\pi\) | |||||||
\(632\) | 22.8133 | + | 15.5104i | 0.907465 | + | 0.616971i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5.02031 | + | 8.05618i | 0.199382 | + | 0.319952i | ||||
\(635\) | 3.89957 | + | 1.41933i | 0.154750 | + | 0.0563242i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.0218106 | − | 0.123694i | 0.000864167 | − | 0.00490094i | ||||
\(638\) | 2.53251 | − | 17.8605i | 0.100263 | − | 0.707104i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −34.1652 | − | 17.0287i | −1.35050 | − | 0.673118i | ||||
\(641\) | −18.2093 | + | 21.7010i | −0.719223 | + | 0.857136i | −0.994555 | − | 0.104213i | \(-0.966768\pi\) |
0.275332 | + | 0.961349i | \(0.411212\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.69392 | − | 0.651338i | 0.145674 | − | 0.0256863i | −0.100336 | − | 0.994954i | \(-0.531992\pi\) |
0.246010 | + | 0.969267i | \(0.420881\pi\) | |||||||
\(644\) | −1.50980 | + | 2.06736i | −0.0594943 | + | 0.0814652i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10.5244 | − | 32.2560i | 0.414078 | − | 1.26909i | ||||
\(647\) | 44.7799 | 1.76048 | 0.880239 | − | 0.474530i | \(-0.157382\pi\) | ||||
0.880239 | + | 0.474530i | \(0.157382\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.0782 | −0.474112 | ||||||||
\(650\) | −1.64732 | + | 5.04883i | −0.0646133 | + | 0.198031i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.28214 | − | 4.49422i | 0.128539 | − | 0.176007i | ||||
\(653\) | 33.2582 | − | 5.86432i | 1.30149 | − | 0.229489i | 0.520411 | − | 0.853916i | \(-0.325779\pi\) |
0.781083 | + | 0.624427i | \(0.214667\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −38.2817 | + | 45.6223i | −1.49579 | + | 1.78261i | ||||
\(656\) | 12.8400 | + | 0.511561i | 0.501316 | + | 0.0199731i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.654888 | − | 4.61860i | 0.0255302 | − | 0.180052i | ||||
\(659\) | −5.48543 | + | 31.1094i | −0.213682 | + | 1.21185i | 0.669497 | + | 0.742815i | \(0.266510\pi\) |
−0.883179 | + | 0.469036i | \(0.844601\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.54548 | + | 1.65442i | 0.176799 | + | 0.0643495i | 0.428903 | − | 0.903351i | \(-0.358900\pi\) |
−0.252104 | + | 0.967700i | \(0.581123\pi\) | |||||||
\(662\) | −9.88016 | − | 15.8549i | −0.384003 | − | 0.616217i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −28.5983 | + | 42.0636i | −1.10983 | + | 1.63238i | ||||
\(665\) | 25.6275 | − | 14.7960i | 0.993791 | − | 0.573765i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.80408 | − | 1.04159i | −0.0698542 | − | 0.0403304i | ||||
\(668\) | 12.4894 | − | 25.4481i | 0.483228 | − | 0.984616i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −42.6547 | − | 22.7472i | −1.64789 | − | 0.878799i | ||||
\(671\) | 1.23065 | − | 1.03264i | 0.0475088 | − | 0.0398646i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.9411 | + | 7.62193i | −0.807220 | + | 0.293804i | −0.712475 | − | 0.701698i | \(-0.752426\pi\) |
−0.0947448 | + | 0.995502i | \(0.530204\pi\) | |||||||
\(674\) | −16.8719 | + | 21.5404i | −0.649880 | + | 0.829705i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.06223 | + | 24.5713i | 0.233163 | + | 0.945050i | ||||
\(677\) | 0.302359 | + | 0.830725i | 0.0116206 | + | 0.0319274i | 0.945367 | − | 0.326007i | \(-0.105703\pi\) |
−0.933747 | + | 0.357934i | \(0.883481\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.2798 | − | 21.7850i | −0.701514 | − | 0.836032i | ||||
\(680\) | −17.2136 | + | 67.9718i | −0.660111 | + | 2.60660i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.96054 | − | 23.4793i | −0.189949 | − | 0.899069i | ||||
\(683\) | −13.1484 | + | 22.7737i | −0.503110 | + | 0.871412i | 0.496883 | + | 0.867817i | \(0.334478\pi\) |
−0.999994 | + | 0.00359510i | \(0.998856\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.5101 | − | 30.3285i | −0.669028 | − | 1.15879i | ||||
\(686\) | −19.1772 | + | 17.2246i | −0.732189 | + | 0.657640i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.978120 | + | 7.21681i | 0.0372905 | + | 0.275138i | ||||
\(689\) | −1.48292 | + | 4.07429i | −0.0564947 | + | 0.155218i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.8477 | + | 4.73397i | 1.02133 | + | 0.180089i | 0.659145 | − | 0.752016i | \(-0.270918\pi\) |
0.362189 | + | 0.932105i | \(0.382029\pi\) | |||||||
\(692\) | 1.70960 | + | 1.77907i | 0.0649893 | + | 0.0676302i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.75393 | − | 16.7759i | −0.256376 | − | 0.636803i | ||||
\(695\) | −56.4077 | − | 47.3317i | −2.13967 | − | 1.79539i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.09864 | − | 23.2446i | −0.155247 | − | 0.880450i | ||||
\(698\) | 0.576864 | + | 17.1223i | 0.0218346 | + | 0.648087i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −28.4796 | + | 19.1081i | −1.07643 | + | 0.722218i | ||||
\(701\) | 0.940626i | 0.0355270i | 0.999842 | + | 0.0177635i | \(0.00565459\pi\) | ||||
−0.999842 | + | 0.0177635i | \(0.994345\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.4188i | 0.392954i | ||||||||
\(704\) | −20.5312 | − | 11.1115i | −0.773799 | − | 0.418781i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 28.2250 | − | 0.950925i | 1.06226 | − | 0.0357885i | ||||
\(707\) | 3.98887 | + | 22.6220i | 0.150017 | + | 0.850789i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.4140 | + | 23.0031i | 1.02956 | + | 0.863899i | 0.990798 | − | 0.135349i | \(-0.0432157\pi\) |
0.0387572 | + | 0.999249i | \(0.487660\pi\) | |||||||
\(710\) | −5.45786 | + | 2.19733i | −0.204830 | + | 0.0824641i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 15.6359 | − | 1.58517i | 0.585981 | − | 0.0594066i | ||||
\(713\) | −2.72915 | − | 0.481223i | −0.102208 | − | 0.0180219i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.98072 | + | 5.44199i | −0.0740749 | + | 0.203519i | ||||
\(716\) | 3.67989 | − | 34.2032i | 0.137524 | − | 1.27823i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 19.8940 | + | 22.1491i | 0.742436 | + | 0.826598i | ||||
\(719\) | −16.5947 | − | 28.7429i | −0.618879 | − | 1.07193i | −0.989691 | − | 0.143221i | \(-0.954254\pi\) |
0.370812 | − | 0.928708i | \(-0.379079\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.7726 | + | 39.4434i | −0.848097 | + | 1.46895i | ||||
\(722\) | 11.5356 | − | 2.43716i | 0.429310 | − | 0.0907016i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 39.5726 | − | 17.5025i | 1.47070 | − | 0.650474i | ||||
\(725\) | −17.9391 | − | 21.3789i | −0.666240 | − | 0.793994i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.0347 | + | 30.3175i | 0.409253 | + | 1.12441i | 0.957585 | + | 0.288153i | \(0.0930410\pi\) |
−0.548331 | + | 0.836261i | \(0.684737\pi\) | |||||||
\(728\) | 1.83238 | − | 4.07511i | 0.0679125 | − | 0.151034i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8.87122 | − | 6.94853i | −0.328339 | − | 0.257177i | ||||
\(731\) | 12.5703 | − | 4.57522i | 0.464929 | − | 0.169220i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.6290 | − | 28.2180i | 1.24211 | − | 1.04226i | 0.244758 | − | 0.969584i | \(-0.421291\pi\) |
0.997356 | − | 0.0726730i | \(-0.0231530\pi\) | |||||||
\(734\) | 18.5252 | − | 34.7378i | 0.683777 | − | 1.28219i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.07579 | + | 1.72018i | −0.0765147 | + | 0.0634067i | ||||
\(737\) | −25.6023 | − | 14.7815i | −0.943071 | − | 0.544482i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.8213 | − | 8.55709i | 0.545211 | − | 0.314778i | −0.201977 | − | 0.979390i | \(-0.564737\pi\) |
0.747188 | + | 0.664613i | \(0.231403\pi\) | |||||||
\(740\) | −1.44917 | − | 21.4824i | −0.0532724 | − | 0.789708i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −23.7631 | + | 14.8083i | −0.872371 | + | 0.543629i | ||||
\(743\) | 41.1116 | + | 14.9634i | 1.50824 | + | 0.548954i | 0.958179 | − | 0.286170i | \(-0.0923822\pi\) |
0.550061 | + | 0.835124i | \(0.314604\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.18800 | − | 12.4087i | 0.0801620 | − | 0.454621i | ||||
\(746\) | −8.35873 | − | 1.18522i | −0.306035 | − | 0.0433938i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −11.9207 | + | 41.1901i | −0.435863 | + | 1.50606i | ||||
\(749\) | 6.44753 | − | 7.68387i | 0.235588 | − | 0.280762i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.87467 | − | 1.03586i | 0.214370 | − | 0.0377992i | −0.0654317 | − | 0.997857i | \(-0.520842\pi\) |
0.279801 | + | 0.960058i | \(0.409731\pi\) | |||||||
\(752\) | 1.86262 | − | 4.54570i | 0.0679226 | − | 0.165765i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.45659 | + | 1.12781i | 0.125882 | + | 0.0410725i | ||||
\(755\) | −49.2554 | −1.79259 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.2521 | 1.20857 | 0.604284 | − | 0.796769i | \(-0.293459\pi\) | ||||
0.604284 | + | 0.796769i | \(0.293459\pi\) | |||||||
\(758\) | 19.1443 | + | 6.24637i | 0.695353 | + | 0.226879i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 29.9877 | − | 8.47936i | 1.08777 | − | 0.307579i | ||||
\(761\) | 4.94688 | − | 0.872268i | 0.179324 | − | 0.0316197i | −0.0832649 | − | 0.996527i | \(-0.526535\pi\) |
0.262589 | + | 0.964908i | \(0.415424\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.3104 | − | 21.8215i | 0.662880 | − | 0.789990i | ||||
\(764\) | −9.16765 | − | 2.65317i | −0.331674 | − | 0.0959885i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −22.4038 | − | 3.17672i | −0.809482 | − | 0.114780i | ||||
\(767\) | 0.422740 | − | 2.39748i | 0.0152642 | − | 0.0865678i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −48.6273 | − | 17.6989i | −1.75355 | − | 0.638239i | −0.753725 | − | 0.657189i | \(-0.771745\pi\) |
−0.999820 | + | 0.0189509i | \(0.993967\pi\) | |||||||
\(770\) | −31.7402 | + | 19.7793i | −1.14384 | + | 0.712796i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −18.0789 | + | 1.21957i | −0.650674 | + | 0.0438934i | ||||
\(773\) | −8.36174 | + | 4.82765i | −0.300751 | + | 0.173639i | −0.642780 | − | 0.766051i | \(-0.722219\pi\) |
0.342029 | + | 0.939689i | \(0.388886\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −32.1524 | − | 18.5632i | −1.15495 | − | 0.666811i | ||||
\(776\) | −13.0293 | − | 26.9657i | −0.467723 | − | 0.968012i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11.8453 | − | 22.2118i | 0.424673 | − | 0.796333i | ||||
\(779\) | −8.03605 | + | 6.74305i | −0.287921 | + | 0.241595i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.38111 | + | 1.23062i | −0.120986 | + | 0.0440352i | ||||
\(782\) | 3.89836 | + | 3.05345i | 0.139405 | + | 0.109191i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.756161 | − | 0.397305i | 0.0270058 | − | 0.0141894i | ||||
\(785\) | 19.2397 | + | 52.8607i | 0.686695 | + | 1.88668i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.8465 | − | 30.8027i | −0.921329 | − | 1.09800i | −0.994916 | − | 0.100709i | \(-0.967889\pi\) |
0.0735865 | − | 0.997289i | \(-0.476555\pi\) | |||||||
\(788\) | 1.68369 | + | 3.80676i | 0.0599788 | + | 0.135610i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 45.5350 | − | 9.62032i | 1.62006 | − | 0.342276i | ||||
\(791\) | 7.84266 | − | 13.5839i | 0.278853 | − | 0.482987i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.161901 | + | 0.280422i | 0.00574929 | + | 0.00995806i | ||||
\(794\) | −17.6611 | − | 19.6632i | −0.626770 | − | 0.697820i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 22.3872 | + | 2.40861i | 0.793494 | + | 0.0853711i | ||||
\(797\) | 1.57213 | − | 4.31940i | 0.0556878 | − | 0.153001i | −0.908730 | − | 0.417385i | \(-0.862947\pi\) |
0.964417 | + | 0.264384i | \(0.0851687\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.88621 | − | 1.56688i | −0.314371 | − | 0.0554322i | ||||
\(800\) | −34.0142 | + | 12.1441i | −1.20258 | + | 0.429358i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −40.5336 | + | 16.3187i | −1.43129 | + | 0.576235i | ||||
\(803\) | −5.27903 | − | 4.42963i | −0.186293 | − | 0.156318i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.749954 | + | 4.25320i | 0.0264324 | + | 0.149906i | ||||
\(806\) | 4.83415 | − | 0.162867i | 0.170276 | − | 0.00573674i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.77639 | + | 24.1255i | −0.0624931 | + | 0.848732i | ||||
\(809\) | − | 17.3051i | − | 0.608415i | −0.952606 | − | 0.304208i | \(-0.901608\pi\) | ||
0.952606 | − | 0.304208i | \(-0.0983917\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.64157i | 0.162987i | 0.996674 | + | 0.0814937i | \(0.0259691\pi\) | ||||
−0.996674 | + | 0.0814937i | \(0.974031\pi\) | |||||||
\(812\) | 13.0820 | + | 19.4981i | 0.459089 | + | 0.684248i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.443370 | − | 13.1599i | −0.0155401 | − | 0.461255i | ||||
\(815\) | −1.63032 | − | 9.24603i | −0.0571078 | − | 0.323874i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.55442 | − | 3.82161i | −0.159339 | − | 0.133701i | ||||
\(818\) | −13.0006 | − | 32.2917i | −0.454554 | − | 1.12905i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 15.6315 | − | 15.0211i | 0.545875 | − | 0.524559i | ||||
\(821\) | 34.5874 | + | 6.09870i | 1.20711 | + | 0.212846i | 0.740769 | − | 0.671759i | \(-0.234461\pi\) |
0.466340 | + | 0.884605i | \(0.345572\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.0707205 | + | 0.194303i | −0.00246516 | + | 0.00677298i | −0.940919 | − | 0.338631i | \(-0.890036\pi\) |
0.938454 | + | 0.345404i | \(0.112258\pi\) | |||||||
\(824\) | −33.4454 | + | 34.3793i | −1.16513 | + | 1.19766i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11.6961 | − | 10.5052i | 0.406958 | − | 0.365523i | ||||
\(827\) | −6.40289 | − | 11.0901i | −0.222650 | − | 0.385642i | 0.732962 | − | 0.680270i | \(-0.238137\pi\) |
−0.955612 | + | 0.294628i | \(0.904804\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.0149 | − | 24.2745i | 0.486757 | − | 0.843088i | −0.513127 | − | 0.858313i | \(-0.671513\pi\) |
0.999884 | + | 0.0152250i | \(0.00484646\pi\) | |||||||
\(830\) | 17.7381 | + | 83.9582i | 0.615699 | + | 2.91423i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.92418 | − | 3.68645i | 0.101378 | − | 0.127805i | ||||
\(833\) | −1.00851 | − | 1.20190i | −0.0349429 | − | 0.0416433i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.3568 | − | 44.9400i | −0.566051 | − | 1.55521i | ||||
\(836\) | 18.5032 | − | 4.56510i | 0.639945 | − | 0.157887i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.94380 | + | 8.86519i | −0.239869 | + | 0.306243i | ||||
\(839\) | −31.3898 | + | 11.4250i | −1.08370 | + | 0.394434i | −0.821283 | − | 0.570521i | \(-0.806741\pi\) |
−0.262415 | + | 0.964955i | \(0.584519\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.57857 | − | 6.35918i | 0.261330 | − | 0.219282i | ||||
\(842\) | −5.12959 | − | 2.73554i | −0.176777 | − | 0.0942729i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −9.88251 | − | 4.85011i | −0.340170 | − | 0.166948i | ||||
\(845\) | 36.9760 | + | 21.3481i | 1.27201 | + | 0.734397i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.77875 | − | 3.33636i | 0.198560 | − | 0.114639i | ||||
\(848\) | −28.0876 | + | 8.97386i | −0.964531 | + | 0.308164i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 35.0856 | + | 56.3025i | 1.20343 | + | 1.93116i | ||||
\(851\) | −1.42888 | − | 0.520068i | −0.0489812 | − | 0.0178277i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.02953 | − | 39.8664i | 0.240686 | − | 1.36500i | −0.589615 | − | 0.807685i | \(-0.700720\pi\) |
0.830301 | − | 0.557315i | \(-0.188169\pi\) | |||||||
\(854\) | −0.293561 | + | 2.07034i | −0.0100455 | + | 0.0708456i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.56865 | − | 6.17737i | 0.292870 | − | 0.211138i | ||||
\(857\) | −9.81314 | + | 11.6948i | −0.335210 | + | 0.399488i | −0.907150 | − | 0.420808i | \(-0.861747\pi\) |
0.571940 | + | 0.820296i | \(0.306191\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.9446 | − | 4.39840i | 0.851098 | − | 0.150071i | 0.268950 | − | 0.963154i | \(-0.413323\pi\) |
0.582148 | + | 0.813083i | \(0.302212\pi\) | |||||||
\(860\) | 9.92221 | + | 7.24622i | 0.338345 | + | 0.247094i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −15.1956 | + | 46.5724i | −0.517563 | + | 1.58626i | ||||
\(863\) | −25.0571 | −0.852954 | −0.426477 | − | 0.904498i | \(-0.640245\pi\) | ||||
−0.426477 | + | 0.904498i | \(0.640245\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.16257 | 0.141532 | ||||||||
\(866\) | 3.75290 | − | 11.5021i | 0.127529 | − | 0.390858i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 25.2250 | + | 18.4219i | 0.856192 | + | 0.625279i | ||||
\(869\) | 28.0292 | − | 4.94231i | 0.950827 | − | 0.167656i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.83014 | − | 4.56458i | 0.129779 | − | 0.154665i | ||||
\(872\) | 24.3342 | − | 17.5432i | 0.824059 | − | 0.594086i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.308973 | − | 2.17903i | 0.0104512 | − | 0.0737068i | ||||
\(875\) | −2.17894 | + | 12.3574i | −0.0736617 | + | 0.417756i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.3388 | − | 10.3145i | −0.956932 | − | 0.348295i | −0.184101 | − | 0.982907i | \(-0.558937\pi\) |
−0.772830 | + | 0.634613i | \(0.781160\pi\) | |||||||
\(878\) | −5.99200 | − | 9.61547i | −0.202220 | − | 0.324507i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −37.5163 | + | 11.9863i | −1.26468 | + | 0.404059i | ||||
\(881\) | −33.7727 | + | 19.4987i | −1.13783 | + | 0.656927i | −0.945892 | − | 0.324480i | \(-0.894811\pi\) |
−0.191938 | + | 0.981407i | \(0.561477\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.27427 | + | 4.19980i | 0.244799 | + | 0.141335i | 0.617380 | − | 0.786665i | \(-0.288194\pi\) |
−0.372582 | + | 0.927999i | \(0.621527\pi\) | |||||||
\(884\) | −7.75882 | − | 3.80785i | −0.260957 | − | 0.128072i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.91061 | + | 5.28519i | 0.332954 | + | 0.177560i | ||||
\(887\) | 18.2466 | − | 15.3107i | 0.612661 | − | 0.514083i | −0.282826 | − | 0.959171i | \(-0.591272\pi\) |
0.895487 | + | 0.445088i | \(0.146828\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.10406 | + | 1.12979i | −0.104107 | + | 0.0378918i | ||||
\(890\) | 16.3493 | − | 20.8732i | 0.548029 | − | 0.699671i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −10.6067 | + | 2.61688i | −0.355138 | + | 0.0876195i | ||||
\(893\) | 1.37163 | + | 3.76851i | 0.0458997 | + | 0.126108i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −37.3047 | − | 44.4580i | −1.24696 | − | 1.48607i | ||||
\(896\) | 29.5459 | − | 7.09734i | 0.987060 | − | 0.237105i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.252617 | − | 1.19569i | −0.00842994 | − | 0.0399007i | ||||
\(899\) | −12.7090 | + | 22.0126i | −0.423868 | + | 0.734162i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27.0802 | + | 46.9043i | 0.902173 | + | 1.56261i | ||||
\(902\) | 9.86331 | − | 8.85905i | 0.328412 | − | 0.294974i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.5183 | − | 11.8399i | 0.383091 | − | 0.393788i | ||||
\(905\) | 24.9673 | − | 68.5972i | 0.829942 | − | 2.28025i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.3699 | + | 2.35747i | 0.443940 | + | 0.0782785i | 0.391150 | − | 0.920327i | \(-0.372077\pi\) |
0.0527900 | + | 0.998606i | \(0.483189\pi\) | |||||||
\(908\) | −2.14096 | + | 2.05736i | −0.0710503 | + | 0.0682759i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.81519 | − | 6.99256i | −0.0933226 | − | 0.231801i | ||||
\(911\) | 2.94930 | + | 2.47476i | 0.0977147 | + | 0.0819924i | 0.690336 | − | 0.723489i | \(-0.257463\pi\) |
−0.592622 | + | 0.805481i | \(0.701907\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.11271 | + | 51.6808i | 0.301587 | + | 1.71038i | ||||
\(914\) | 1.39853 | + | 41.5107i | 0.0462593 | + | 1.37305i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −29.0332 | − | 43.2725i | −0.959285 | − | 1.42976i | ||||
\(917\) | − | 47.4065i | − | 1.56550i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.14983i | 0.235851i | 0.993022 | + | 0.117926i | \(0.0376244\pi\) | ||||
−0.993022 | + | 0.117926i | \(0.962376\pi\) | |||||||
\(920\) | −0.333981 | + | 4.53587i | −0.0110110 | + | 0.149543i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −8.12393 | + | 0.273703i | −0.267547 | + | 0.00901391i | ||||
\(923\) | −0.125934 | − | 0.714207i | −0.00414516 | − | 0.0235084i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.6052 | − | 13.0943i | −0.513096 | − | 0.430539i | ||||
\(926\) | −36.0910 | + | 14.5301i | −1.18602 | + | 0.477490i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.31423 | + | 23.2872i | 0.272928 | + | 0.764440i | ||||
\(929\) | −24.6142 | − | 4.34015i | −0.807566 | − | 0.142396i | −0.245402 | − | 0.969421i | \(-0.578920\pi\) |
−0.562164 | + | 0.827026i | \(0.690031\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.238498 | + | 0.655267i | −0.00781644 | + | 0.0214755i | ||||
\(932\) | 13.3498 | + | 1.43630i | 0.437289 | + | 0.0470474i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −15.9099 | − | 17.7134i | −0.520586 | − | 0.579600i | ||||
\(935\) | 36.1708 | + | 62.6497i | 1.18291 | + | 2.04886i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.71158 | + | 2.96455i | −0.0559150 | + | 0.0968475i | −0.892628 | − | 0.450794i | \(-0.851141\pi\) |
0.836713 | + | 0.547642i | \(0.184474\pi\) | |||||||
\(938\) | 37.6485 | − | 7.95411i | 1.22927 | − | 0.259711i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.35229 | − | 7.57943i | −0.109340 | − | 0.247214i | ||||
\(941\) | −23.4217 | − | 27.9129i | −0.763525 | − | 0.909934i | 0.234540 | − | 0.972106i | \(-0.424642\pi\) |
−0.998065 | + | 0.0621723i | \(0.980197\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.523637 | − | 1.43868i | −0.0170520 | − | 0.0468499i | ||||
\(944\) | 14.6562 | − | 7.70068i | 0.477017 | − | 0.250636i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.91527 | + | 4.63323i | 0.192322 | + | 0.150639i | ||||
\(947\) | −6.56612 | + | 2.38987i | −0.213370 | + | 0.0776605i | −0.446494 | − | 0.894787i | \(-0.647328\pi\) |
0.233124 | + | 0.972447i | \(0.425105\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.06403 | − | 0.892826i | 0.0345398 | − | 0.0289824i | ||||
\(950\) | 13.8741 | − | 26.0162i | 0.450135 | − | 0.844077i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −24.2821 | − | 50.2549i | −0.786987 | − | 1.62877i | ||||
\(953\) | −6.10328 | − | 3.52373i | −0.197705 | − | 0.114145i | 0.397880 | − | 0.917438i | \(-0.369746\pi\) |
−0.595584 | + | 0.803293i | \(0.703079\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.9439 | + | 8.05052i | −0.451214 | + | 0.260509i | ||||
\(956\) | 40.9005 | − | 2.75908i | 1.32282 | − | 0.0892351i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.65112 | − | 1.65208i | 0.0856536 | − | 0.0533761i | ||||
\(959\) | 26.1951 | + | 9.53424i | 0.845884 | + | 0.307877i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.488585 | + | 2.77090i | −0.0157608 | + | 0.0893840i | ||||
\(962\) | 2.62770 | + | 0.372592i | 0.0847206 | + | 0.0120128i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 24.2625 | + | 7.02172i | 0.781443 | + | 0.226154i | ||||
\(965\) | −19.6497 | + | 23.4176i | −0.632545 | + | 0.753838i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.0009 | − | 4.58465i | 0.836131 | − | 0.147433i | 0.260841 | − | 0.965382i | \(-0.416000\pi\) |
0.575290 | + | 0.817949i | \(0.304889\pi\) | |||||||
\(968\) | 6.76194 | − | 1.91201i | 0.217337 | − | 0.0614544i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −48.0327 | − | 15.6720i | −1.54224 | − | 0.503199i | ||||
\(971\) | 34.6797 | 1.11292 | 0.556462 | − | 0.830873i | \(-0.312159\pi\) | ||||
0.556462 | + | 0.830873i | \(0.312159\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 58.6137 | 1.87907 | ||||||||
\(974\) | 54.4317 | + | 17.7599i | 1.74410 | + | 0.569063i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.834940 | + | 2.03766i | −0.0267258 | + | 0.0652240i | ||||
\(977\) | −44.4064 | + | 7.83005i | −1.42069 | + | 0.250505i | −0.830616 | − | 0.556846i | \(-0.812011\pi\) |
−0.590071 | + | 0.807351i | \(0.700900\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.4225 | − | 12.4211i | 0.333106 | − | 0.396980i | ||||
\(980\) | 0.400612 | − | 1.38425i | 0.0127971 | − | 0.0442184i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 22.1552 | + | 3.14147i | 0.707002 | + | 0.100248i | ||||
\(983\) | 6.89149 | − | 39.0836i | 0.219804 | − | 1.24657i | −0.652568 | − | 0.757731i | \(-0.726308\pi\) |
0.872372 | − | 0.488843i | \(-0.162581\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.59884 | + | 2.40178i | 0.210257 | + | 0.0765272i | ||||
\(986\) | 38.5465 | − | 24.0207i | 1.22757 | − | 0.764976i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.258539 | + | 3.83257i | 0.00822522 | + | 0.121930i | ||||
\(989\) | 0.751448 | − | 0.433849i | 0.0238947 | − | 0.0137956i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.9550 | + | 9.78895i | 0.538592 | + | 0.310956i | 0.744508 | − | 0.667613i | \(-0.232684\pi\) |
−0.205916 | + | 0.978570i | \(0.566017\pi\) | |||||||
\(992\) | 20.9889 | + | 25.3279i | 0.666398 | + | 0.804162i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.20378 | − | 4.13244i | 0.0698995 | − | 0.131073i | ||||
\(995\) | 29.0993 | − | 24.4172i | 0.922511 | − | 0.774078i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35.2892 | − | 12.8442i | 1.11762 | − | 0.406780i | 0.283837 | − | 0.958873i | \(-0.408393\pi\) |
0.833783 | + | 0.552092i | \(0.186170\pi\) | |||||||
\(998\) | 37.2476 | + | 29.1748i | 1.17905 | + | 0.923512i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 324.2.l.a.143.7 | 96 | ||
3.2 | odd | 2 | 108.2.l.a.47.10 | yes | 96 | ||
4.3 | odd | 2 | inner | 324.2.l.a.143.13 | 96 | ||
9.2 | odd | 6 | 972.2.l.d.107.2 | 96 | |||
9.4 | even | 3 | 972.2.l.b.755.5 | 96 | |||
9.5 | odd | 6 | 972.2.l.c.755.12 | 96 | |||
9.7 | even | 3 | 972.2.l.a.107.15 | 96 | |||
12.11 | even | 2 | 108.2.l.a.47.4 | yes | 96 | ||
27.4 | even | 9 | 108.2.l.a.23.4 | ✓ | 96 | ||
27.5 | odd | 18 | 972.2.l.b.215.3 | 96 | |||
27.13 | even | 9 | 972.2.l.d.863.8 | 96 | |||
27.14 | odd | 18 | 972.2.l.a.863.9 | 96 | |||
27.22 | even | 9 | 972.2.l.c.215.14 | 96 | |||
27.23 | odd | 18 | inner | 324.2.l.a.179.13 | 96 | ||
36.7 | odd | 6 | 972.2.l.a.107.9 | 96 | |||
36.11 | even | 6 | 972.2.l.d.107.8 | 96 | |||
36.23 | even | 6 | 972.2.l.c.755.14 | 96 | |||
36.31 | odd | 6 | 972.2.l.b.755.3 | 96 | |||
108.23 | even | 18 | inner | 324.2.l.a.179.7 | 96 | ||
108.31 | odd | 18 | 108.2.l.a.23.10 | yes | 96 | ||
108.59 | even | 18 | 972.2.l.b.215.5 | 96 | |||
108.67 | odd | 18 | 972.2.l.d.863.2 | 96 | |||
108.95 | even | 18 | 972.2.l.a.863.15 | 96 | |||
108.103 | odd | 18 | 972.2.l.c.215.12 | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.2.l.a.23.4 | ✓ | 96 | 27.4 | even | 9 | ||
108.2.l.a.23.10 | yes | 96 | 108.31 | odd | 18 | ||
108.2.l.a.47.4 | yes | 96 | 12.11 | even | 2 | ||
108.2.l.a.47.10 | yes | 96 | 3.2 | odd | 2 | ||
324.2.l.a.143.7 | 96 | 1.1 | even | 1 | trivial | ||
324.2.l.a.143.13 | 96 | 4.3 | odd | 2 | inner | ||
324.2.l.a.179.7 | 96 | 108.23 | even | 18 | inner | ||
324.2.l.a.179.13 | 96 | 27.23 | odd | 18 | inner | ||
972.2.l.a.107.9 | 96 | 36.7 | odd | 6 | |||
972.2.l.a.107.15 | 96 | 9.7 | even | 3 | |||
972.2.l.a.863.9 | 96 | 27.14 | odd | 18 | |||
972.2.l.a.863.15 | 96 | 108.95 | even | 18 | |||
972.2.l.b.215.3 | 96 | 27.5 | odd | 18 | |||
972.2.l.b.215.5 | 96 | 108.59 | even | 18 | |||
972.2.l.b.755.3 | 96 | 36.31 | odd | 6 | |||
972.2.l.b.755.5 | 96 | 9.4 | even | 3 | |||
972.2.l.c.215.12 | 96 | 108.103 | odd | 18 | |||
972.2.l.c.215.14 | 96 | 27.22 | even | 9 | |||
972.2.l.c.755.12 | 96 | 9.5 | odd | 6 | |||
972.2.l.c.755.14 | 96 | 36.23 | even | 6 | |||
972.2.l.d.107.2 | 96 | 9.2 | odd | 6 | |||
972.2.l.d.107.8 | 96 | 36.11 | even | 6 | |||
972.2.l.d.863.2 | 96 | 108.67 | odd | 18 | |||
972.2.l.d.863.8 | 96 | 27.13 | even | 9 |